It has long been known that all electrical resistors are characterized by an inherent noise which is due to the thermal agitation of the free electrons within the resistor material. As used herein, the term "resistor", includes any body of conductive material capable of carrying an electrical current. As such, the term embraces components such as wires and other conductors which are not ordinarily thought of "resistors". If a signal current in the resistor or conductor is smaller than the random current due to thermal agitation then, as practical matter, the signal is masked by the noise and no amount of amplification can separate them. This noise, known as "thermal noise", "Johnson noise" or "white noise", has heretofore generally been accepted as one of the limiting factors in the design of low-level signal processing circuits.
From the research of Johnson and Nyquist in the late 1920s, it is known that the thermal noise voltage across the open ends of a resistor is determined by the formula: EQU N.sup.2 =4kTRB [1]
Where N.sup.2 is the average of the square of the noise voltage; k is Boltzmann's constant (1.38.times.10.sup.-23 joules per .degree.K.); T is the absolute temperature of the conductor in .degree.K.; R is the resistance of the resistor or conductor in ohms and B is the bandwidth in Hertz over which the noise is measured.
In order to reduce the thermal noise of a given resistance R, it is seen from Equation [1] that either the temperature (T) or the bandwidth (B) must be reduced. In general, therefore, it has been the practice to minimize the thermal noise by cooling the resistor or the entire circuit, in some cases to cryogenic temperatures. However, since the noise voltage is proportional to the square root of the temperature, it is readily understood that it is both costly and cumbersome to provide the degree of cooling required to achieve a significant reduction in thermal noise.
It is therefore an object of the present invention to provide a non-cryogenically cooled low-noise-temperature resistance.
In 1939, it was suggested by W.S. Percival that a simulated resistor having an effective noise temperature lower than ambient temperature could be realized by feedback means. (See: W.S. Percival, An Electrically "Cold" Resistance, the Wireless Engineer, Vol. 16, May 1939, pp. 237-240.) Utilizing a single transformer between the plate and grid circuit of a vacuum tube amplifier, Percival simulated a resistance having an effective temperature of 70.degree. K. The same technique was later expanded upon by Strutt and Van der Ziel in an article entitled, "Suppression of Spontaneous Fluctuations in Amplifiers and Receivers for Electrical Communication and for Measuring Devices", Physica, Vol. 9, No. 6, June 1942, pp. 513, 527. Professor Van der Ziel also briefly summarized the techniques in his treatise "Noise", Prentice-Hall, New York, N.Y. 1954, pp. 281-283. (See also: U.S. Pat. No. 2,352,956; M. J. O. Strutt, et al.; July 4, 1944.)
The circuits of the prior art appear to have received little attention in the several decades since their introduction. This may be due to the many shortcomings in the use of vacuum tubes such as their high operating temperatures and the other sources of noise inherent therein. In any event, recent advances in solid state technology have produced many sophisticated, highly efficient, low-cost active circuit elements which allow the synthesis of economical low-noise-temperature resistance simulating circuits.
It is yet another object of the present invention to provide an active circuit which simulates a low-noise resistor.
In several copending applications filed on behalf of the applicant R. L. Forward, either solely or with others, there are disclosed several classes of circuits which simulate low noise-temperature resistors. In application Ser. No. 838,511 filed Oct. 3, 1977 now U.S. Pat. No. 4,156,859 there is disclosed a class of active circuits utilizing operational amplifiers with one or more transformers forming the intra-circuit interconnections. Another copending application Ser. No. 881,296, filed Feb. 27, 1978 now U.S. Pat. No. 4,176,331 also utilizes operational amplifiers but with a resistive voltage divider network comprising the remainder of the circuit. Application Ser. No. 018,688, filed Mar. 8, 1979 utilized field effect transistors in the preferred embodiment. All of the aforesaid copending applications are characterized by advantages which lend themselves to particular uses. Depending upon the requirements of the job at hand, any of the above-mentioned classes of circuits may be advantageously employed.